# B Light and its ideal speed

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1. Jul 21, 2017

### stoomart

When I read the speed of light in vacuum is c, does it imply that light doesn't actually travel at this speed in nature? My guess is no, light always travels at c, it's just that in the definition, we're trying to ignore the affects on light from other stuff like the comological constant and the stress-energy tensor.

2. Jul 21, 2017

### Staff: Mentor

It does travel at c in nature, in a vacuum. It is slower in a medium:
https://en.wikipedia.org/wiki/Refractive_index
I'm not sure if this is still the record holder, I thought I've read of even a slower experiment, but it's impressing anyway:
https://en.wikipedia.org/wiki/Slow_light

3. Jul 21, 2017

### stoomart

4. Jul 21, 2017

### Staff: Mentor

Yes, but the few particles in space are so rare, that they hardly would be in the path of a light ray. The question then would be: Does space have a measurable refractive index different from 1? I don't think so.

5. Jul 22, 2017

### stoomart

That makes sense, and also brings up the question of whether pressure or other factors in the radiation or matter-dominated eras may have directly affected the speed light traveled, even temporarily like a medium does.

Last edited: Jul 22, 2017
6. Jul 22, 2017

### Ibix

Difficult to answer simply, because it depends what you mean by "speed" and what you mean by "speed of light".

In practice the universe was opaque due to the high density. So the speed of light in the sense of "I set up a flash lamp and a mirror, what time does the pulse return" isn't defined, just as the speed of light in a lump of lead isn't really defined.

That said, if (BIG if) you could clear a small volume, you would find that the speed of light was c. This is because spacetime is always locally flat and special relativity applies.

But if (really ginormous if) you cleared a large volume the effects of curvature would become apparent and it's not possible to define velocity in an unambiguous way across the whole volume. In that case the speed of light depends on how you choose to define it.

Possibly the best answer is the local one. The significance of c is that it is a natural conversion factor between units of distance and units of time. It's almost irrelevant to relativity that light travels at c in vacuum.

7. Jul 22, 2017

Staff Emeritus
"We define c to be the speed of light in vacuum but there are no perfect vacua" is the same complaint that there are no frictionless planes or massless pulleys. It's a complaint that leads nowhere, and certainly not to a better understanding.

Oh, and the speed of light in lead is about 1200 km/s.

8. Jul 22, 2017

### ZapperZ

Staff Emeritus
Then how do you explain the CODATA exact determination of "c"?

Zz.

9. Jul 22, 2017

### stoomart

Not a complaint, but a question has been nagging me for the last few weeks as I've been considering the CMBR, whether any refractive index exists in space that must be accounted for. Per the following, would it be incorrect to say an imperfect vacuum has a refractive index of >1?

The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and that the frequency (f = v/λ) of the wave is not affected by the refractive index.​

The 2006 CODATA recommendations refer to the BIPM for constants with exact values by definition:

Section II touches on special quantities and units, that is, those that have exact values by definition.​

Table I lists those quantities whose numerical values are exactly defined. In the International System of Units (SI) (BIPM, 2006), used throughout this paper, the definition of the meter fixes the speed of light in vacuum c

Last edited: Jul 22, 2017
10. Jul 22, 2017

### ZapperZ

Staff Emeritus
Yeah, and those values are obtained how? Out of the air (pun intended)?

Every single one of the CODATA values are obtained out of experiments, or derived from them. If we have never had experienced a "true vacuum", as you insisted, then the CODATA values for "c" can never have been obtained in a true vacuum either. Yet, this is how the standards have been defined.

Zz.

11. Jul 22, 2017

### stoomart

I want to clarify that the intention of this thread is not to debate the speed of light as a constant, but to understand if light travels slower in the absence of a "true vacuum". It seems the use of "exact" in defining the speed of light is a bit of a stretch (pun intended:), given a measurement uncertainty of 4 parts per billion:

considering the excellent agreement among the results of wavelength measurements on the radiations of lasers locked on a molecular absorption line in the visible or infrared region, with an uncertainty estimated at ± 4 x 10–9 which corresponds to the uncertainty of the realization of the metre,

considering also the concordant measurements of the frequencies of several of these radiations,

recommends the use of the resulting value for the speed of propagation of electromagnetic waves in vacuum c = 299 792 458 metres per second.

Note: The relative uncertainty given here corresponds to three standard deviations in the data considered.​

12. Jul 22, 2017

Staff Emeritus
This is getting silly.

Point the first: Do you not agree that you cannot have three independent definitions for the meter, the second and the meter per second (without risking inconsistency)? So what is the problem with picking the second and the meter per second as the units that will be set by definition?

Point the second: The speed of light in intergalactic space differs from c by about a micron per century. Traversing the entire universe, the non-perfect vacuum of space slows light by only a microsecond. Your quibble makes no difference.

Point the third: even if it is impossible to reach perfect vacuum, one can still determine the speed of light there, by measuring the speed of light in media of varying density, plotting the curve, and seeing where it intersects zero.

13. Jul 22, 2017

### kimbyd

The normal matter density at the time the CMB was emitted would have been roughly $1\times 10^{-18} kg/m^3$. The density of air at sea level is roughly $1.2 kg/m^3$. The speed of light is changed by a factor of about one part in a million in our atmosphere. The difference is going to be utterly negligible when the CMB is emitted.

14. Jul 22, 2017

### stoomart

Thanks V, this is what I was looking for, sorry for the silly quibble.